929 resultados para In-plane Shear Equations


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In this paper we analyze the structure of Fe-Ga layers with a Ga content of ∼30 at.% deposited by the sputtering technique under two different regimes. We also studied the correlation between the structure and magnetic behavior of the samples. Keeping the Ar pressure fixed, we modified the flow regime from ballistic to diffusive by increasing the distance between the target and the substrate. X-ray diffraction measurements have shown a lower structural quality when growing in the diffusive flow. We investigated the impact of the growth regime by means of x-ray absorption fine structure (XAFS) measurements and obtained signs of its influence on the local atomic order. Full multiple scattering and finite difference calculations based on XAFS measurements point to a more relevant presence of a disordered A2 phase and of orthorhombic Ga clusters on the Fe-Ga alloy deposited under a diffusive regime; however, in the ballistic sample, a higher presence of D0_3/B2 phases is evidenced. Structural characteristics, from local to long range, seem to determine the magnetic behavior of the layers. Whereas a clear in-plane magnetic anisotropy is observed in the film deposited under ballistic flow, the diffusive sample is magnetically isotropic. Therefore, our experimental results provide evidence of a correlation between flow regime and structural properties and its impact on the magnetic behavior of a rather unexplored compositional region of Fe-Ga compounds.

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c-axis oriented ferroelectric bismuth titanate (Bi4Ti 3O12) thin films were grown on (001) strontium titanate (SrTiO3) substrates by an atomic vapor deposition technique. The ferroelectric properties of the thin films are greatly affected by the presence of various kinds of defects. Detailed x-ray diffraction data and transmission electron microscopy analysis demonstrated the presence of out-of-phase boundaries (OPBs). It is found that the OPB density changes appreciably with the amount of titanium injected during growth of the thin films. Piezo-responses of the thin films were measured by piezo-force microscopy. It is found that the in-plane piezoresponse is stronger than the out-of-plane response, due to the strong c-axis orientation of the films.

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The deposition by atomic vapor deposition of highly c-axis-oriented Aurivillius phase Bi 5Ti 3FeO 15 (BTFO) thin films on (100) Si substrates is reported. Partially crystallized BTFO films with c-axis perpendicular to the substrate surface were first deposited at 610°C (8 excess Bi), and subsequently annealed at 820°C to get stoichiometric composition. After annealing, the films were highly c-axis-oriented, showing only (00l) peaks in x-ray diffraction (XRD), up to (0024). Transmission electron microscopy (TEM) confirms the BTFO film has a clear layered structure, and the bismuth oxide layer interleaves the four-block pseudoperovskite layer, indicating the n 4 Aurivillius phase structure. Piezoresponse force microscopy measurements indicate strong in-plane piezoelectric response, consistent with the c-axis layered structure, shown by XRD and TEM.

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Aurivillius phase Bi 5Ti 3Fe 0.7Co 0.3O 15 (BTF7C3O) thin films on α-quartz substrates were fabricated by a chemical solution deposition method and the room temperature ferroelectric and magnetic properties of this candidate multiferroic were compared with those of thin films of Mn 3 substituted, Bi 5Ti 3Fe 0.7Mn 0.3O 15 (BTF7M3O). Vertical and lateral piezoresponse force microscopy (PFM) measurements of the films conclusively demonstrate that BTF7C3O and BTF7M3O thin films are piezoelectric and ferroelectric at room temperature, with the major polarization vector in the lateral plane of the films. No net magnetization was observed for the in-plane superconducting quantum interference device (SQUID) magnetometry measurements of BTF7M3O thin films. In contrast, SQUID measurements of the BTF7C3O films clearly demonstrated ferromagnetic behavior, with a remanent magnetization, B r, of 6.37 emu/cm 3 (or 804 memu/g), remanent moment 4.99 × 10 -5 emu. The BTF7C3O films were scrutinized by x-ray diffraction, high resolution transmission electron microscopy, scanning transmission electron microscopy, and energy dispersive x-ray analysis mapping to assess the prospect of the observed multiferroic properties being intrinsic to the main phase. The results of extensive micro-structural phase analysis demonstrated that the BTF7C3O films comprised of a 3.95 Fe/Co-rich spinel phase, likely CoFe 2 - xTi xO 4, which would account for the observed magnetic moment in the films. Additionally, x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) imaging confirmed that the majority of magnetic response arises from the Fe sites of Fe/Co-rich spinel phase inclusions. While the magnetic contribution from the main phase could not be determined by the XMCD-PEEM images, these data however imply that the Bi 5Ti 3Fe 0.7Co 0.3O 15 thin films are likely not single phase multiferroics at room temperature. The PFM results presented demonstrate that the naturally 2D nanostructured Bi 5Ti 3Fe 0.7Co 0.3O 15 phase is a novel ferroelectric and has potential commercial applications in high temperature piezoelectric and ferroelectric memory technologies. The implications for the conclusive demonstration of ferroelectric and ferromagnetic properties in single-phase materials of this type are discussed.

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Factor-of-safety analyses of submarine slope failure depend critically on the shear strength of the slope material, which is often evaluated with residual strength values and for normally consolidated sediments. Here, we report on direct measurements of both shear strength and cohesion for a quartz-clay mixture over a wide range of overconsolidation ratios (OCRs). For normally consolidated sediment at low stresses, cohesion is the dominant source of shear strength compared to friction. Significant increases in peak shear strength occur for OCR > 4, and the primary source of this strength increase is due to increased cohesion, rather than friction. The proportion of added shear strength due to cohesion depends log-linearly on the OCR. We show that at shallow depths where OCR values can be high, overconsolidated clays can be stronger than pure or nearly pure quartz sediments, which are cohesionless under near-surface conditions. Our data also suggest that areas which have experienced significant unroofing due to previous mass movements are less likely to experience subsequent failure at shallow depths due to increased peak strength, and if failure occurs it is expected to be deeper where the OCR is lower. In seismically active areas, this is one potential explanation for the general observation of lower slope failure recurrence compared to rates expected from triggering due to local earthquakes.

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With ever increasing demands to strengthen existing reinforced concrete structures to facilitate higher loading due to change of use and to extend service lifetime, the use of fibre reinforced polymers (FRPs) in structural retrofitting offers an opportunity to achieve these aims. To date, most research in this area has focussed on the use of glass fibre reinforced polymer (GFRP) and carbon fibre reinforced polymer (CFRP), with relatively little on the use of basalt fibre reinforced polymer (BFRP) as a suitable strengthening material. In addition, most previous research has been carried out using simply supported elements, which have not considered the beneficial influence of in-plane lateral restraint, as experienced within a framed building structure. Furthermore, by installing FRPs using the near surface mounted (NSM) technique, disturbance to the existing structure can be minimised.
This paper outlines BFRP NSM strengthening of one third scale laterally restrained floor slabs which reflect the inherent insitu compressive membrane action (CMA) in such slabs. The span-to-depth ratios of the test slabs were 20 and 15 and all were constructed with normal strength concrete (~40N/mm2) and 0.15% steel reinforcement. 0.10% BFRP was used in the retrofitted samples, which were compared with unretrofitted control samples. In addition, the bond strength of BFRP bars bonded into concrete was investigated over a range of bond lengths with two different adhesive thicknesses. This involved using an articulated beam arrangement in order to establish optimum bond characteristics for use in strengthening slab samples.

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Abstract : The structural build-up of fresh cement-based materials has a great impact on their structural performance after casting. Accordingly, the mixture design should be tailored to adapt the kinetics of build-up given the application on hand. The rate of structural build-up of cement-based suspensions at rest is a complex phenomenon affected by both physical and chemical structuration processes. The structuration kinetics are strongly dependent on the mixture’s composition, testing parameters, as well as the shear history. Accurate measurements of build-up rely on the efficiency of the applied pre-shear regime to achieve an initial well-dispersed state as well as the applied stress during the liquid-solid transition. Studying the physical and chemical mechanisms of build-up of cement suspensions at rest can enhance the fundamental understanding of this phenomenon. This can, therefore, allow a better control of the rheological and time-dependent properties of cement-based materials. The research focused on the use of dynamic rheology in investigating the kinetics of structural build-up of fresh cement pastes. The research program was conducted in three different phases. The first phase was devoted to evaluating the dispersing efficiency of various disruptive shear techniques. The investigated shearing profiles included rotational, oscillatory, and combination of both. The initial and final states of suspension’s structure, before and after disruption, were determined by applying a small-amplitude oscillatory shear (SAOS). The difference between the viscoelastic values before and after disruption was used to express the degree of dispersion. An efficient technique to disperse concentrated cement suspensions was developed. The second phase aimed to establish a rheometric approach to dissociate and monitor the individual physical and chemical mechanisms of build-up of cement paste. In this regard, the non-destructive dynamic rheometry was used to investigate the evolutions of both storage modulus and phase angle of inert calcium carbonate and cement suspensions. Two independent build-up indices were proposed. The structural build-up of various cement suspensions made with different cement contents, silica fume replacement percentages, and high-range water reducer dosages was evaluated using the proposed indices. These indices were then compared to the well-known thixotropic index (Athix.). Furthermore, the proposed indices were correlated to the decay in lateral pressure determined for various cement pastes cast in a pressure column. The proposed pre-shearing protocol and build-up indices (phases 1 and 2) were then used to investigate the effect of mixture’s parameters on the kinetics of structural build-up in phase 3. The investigated mixture’s parameters included cement content and fineness, alkali sulfate content, and temperature of cement suspension. Zeta potential, calorimetric, spectrometric measurements were performed to explore the corresponding microstructural changes in cement suspensions, such as inter-particle cohesion, rate of Brownian flocculation, and nucleation rate. A model linking the build-up indices and the microstructural characteristics was developed to predict the build-up behaviour of cement-based suspensions The obtained results showed that oscillatory shear may have a greater effect on dispersing concentrated cement suspension than the rotational shear. Furthermore, the increase in induced shear strain was found to enhance the breakdown of suspension’s structure until a critical point, after which thickening effects dominate. An effective dispersing method is then proposed. This consists of applying a rotational shear around the transitional value between the linear and non-linear variations of the apparent viscosity with shear rate, followed by an oscillatory shear at the crossover shear strain and high angular frequency of 100 rad/s. Investigating the evolutions of viscoelastic properties of inert calcite-based and cement suspensions and allowed establishing two independent build-up indices. The first one (the percolation time) can represent the rest time needed to form the elastic network. On the other hand, the second one (rigidification rate) can describe the increase in stress-bearing capacity of formed network due to cement hydration. In addition, results showed that combining the percolation time and the rigidification rate can provide deeper insight into the structuration process of cement suspensions. Furthermore, these indices were found to be well-correlated to the decay in the lateral pressure of cement suspensions. The variations of proposed build-up indices with mixture’s parameters showed that the percolation time is most likely controlled by the frequency of Brownian collisions, distance between dispersed particles, and intensity of cohesion between cement particles. On the other hand, a higher rigidification rate can be secured by increasing the number of contact points per unit volume of paste, nucleation rate of cement hydrates, and intensity of inter-particle cohesion.

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A 3D printed electromagnetic vibration energy harvester is presented. The motion of the device is in-plane with the excitation vibrations, and this is enabled through the exploitation of a leaf isosceles trapezoidal flexural pivot topology. This topology is ideally suited for systems requiring restricted out-of-plane motion and benefits from being fabricated monolithically. This is achieved by 3D printing the topology with materials having a low flexural modulus. The presented system has a nonlinear softening spring response, as a result of designed magnetic force interactions. A discussion of fatigue performance is presented and it is suggested that whilst fabricating, the raster of the suspension element is printed perpendicular to the flexural direction and that the experienced stress is as low as possible during operation, to ensure longevity. A demonstrated power of ~25 μW at 0.1 g is achieved and 2.9 mW is demonstrated at 1 g. The corresponding bandwidths reach up-to 4.5 Hz. The system's corresponding power density of ~0.48 mW cm−3 and normalised power integral density of 11.9 kg m−3 (at 1 g) are comparable to other in-plane systems found in the literature.

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Biochemical agents, including bacteria and toxins, are potentially dangerous and responsible for a wide variety of diseases. Reliable detection and characterization of small samples is necessary in order to reduce and eliminate their harmful consequences. Microcantilever sensors offer a potential alternative to the state of the art due to their small size, fast response time, and the ability to operate in air and liquid environments. At present, there are several technology limitations that inhibit application of microcantilever to biochemical detection and analysis, including difficulties in conducting temperature-sensitive experiments, material inadequacy resulting in insufficient cell capture, and poor selectivity of multiple analytes. This work aims to address several of these issues by introducing microcantilevers having integrated thermal functionality and by introducing nanocrystalline diamond as new material for microcantilevers. Microcantilevers are designed, fabricated, characterized, and used for capture and detection of cells and bacteria. The first microcantilever type described in this work is a silicon cantilever having highly uniform in-plane temperature distribution. The goal is to have 100 μm square uniformly heated area that can be used for thermal characterization of films as well as to conduct chemical reactions with small amounts of material. Fabricated cantilevers can reach above 300C while maintaining temperature uniformity of 2−4%. This is an improvement of over one order of magnitude over currently available cantilevers. The second microcantilever type is a doped single crystal silicon cantilever having a thin coating of ultrananocrystalline diamond (UNCD). The primary application of such a device is in biological testing, where diamond acts as a stable, electrically isolated reaction surface while silicon layer provides controlled heating with minimum variations in temperature. This work shows that composite cantilevers of this kind are an effective platform for temperature-sensitive biological experiments, such as heat lysing and polymerase chain reaction. The rapid heat-transfer of Si-UNCD cantilever compromised the membrane of NIH 3T3 fibroblast and lysed the cell nucleus within 30 seconds. Bacteria cells, Listeria monocytogenes V7, were shown to be captured with biotinylated heat-shock protein on UNCD surface and 90% of all viable cells exhibit membrane porosity due to high heat in 15 seconds. Lastly, a sensor made solely from UNCD diamond is fabricated with the intention of being used to detect the presence of biological species by means of an integrated piezoresistor or through frequency change monitoring. Since UNCD diamond has not been previously used in piezoresistive applications, temperature-denpendent piezoresistive coefficients and gage factors are determined first. The doped UNCD exhibits a significant piezoresistive effect with gauge factor of 7.53±0.32 and a piezoresistive coefficient of 8.12×10^−12 Pa^−1 at room temperature. The piezoresistive properties of UNCD are constant over the temperature range of 25−200C. 300 μm long cantilevers have the highest sensitivity of 0.186 m-Ohm/Ohm per μm of cantilever end deflection, which is approximately half that of similarly sized silicon cantilevers. UNCD cantilever arrays were fabricated consisting of four sixteen-cantilever arrays of length 20–90 μm in addition to an eight-cantilever array of length 120 μm. Laser doppler vibrometry (LDV) measured the cantilever resonant frequency, which ranged as 218 kHz−5.14 MHz in air and 73 kHz−3.68 MHz in water. The quality factor of the cantilever was 47−151 in air and 18−45 in water. The ability to measure frequencies of the cantilever arrays opens the possibility for detection of individual bacteria by monitoring frequency shift after cell capture.

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The thesis aims to exploit properties of thin films for applications such as spintronics, UV detection and gas sensing. Nanoscale thin films devices have myriad advantages and compatibility with Si-based integrated circuits processes. Two distinct classes of material systems are investigated, namely ferromagnetic thin films and semiconductor oxides. To aid the designing of devices, the surface properties of the thin films were investigated by using electron and photon characterization techniques including Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), grazing incidence X-ray diffraction (GIXRD), and energy-dispersive X-ray spectroscopy (EDS). These are complemented by nanometer resolved local proximal probes such as atomic force microscopy (AFM), magnetic force microscopy (MFM), electric force microscopy (EFM), and scanning tunneling microscopy to elucidate the interplay between stoichiometry, morphology, chemical states, crystallization, magnetism, optical transparency, and electronic properties. Specifically, I studied the effect of annealing on the surface stoichiometry of the CoFeB/Cu system by in-situ AES and discovered that magnetic nanoparticles with controllable areal density can be produced. This is a good alternative for producing nanoparticles using a maskless process. Additionally, I studied the behavior of magnetic domain walls of the low coercivity alloy CoFeB patterned nanowires. MFM measurement with the in-plane magnetic field showed that, compared to their permalloy counterparts, CoFeB nanowires require a much smaller magnetization switching field , making them promising for low-power-consumption domain wall motion based devices. With oxides, I studied CuO nanoparticles on SnO2 based UV photodetectors (PDs), and discovered that they promote the responsivity by facilitating charge transfer with the formed nanoheterojunctions. I also demonstrated UV PDs with spectrally tunable photoresponse with the bandgap engineered ZnMgO. The bandgap of the alloyed ZnMgO thin films was tailored by varying the Mg contents and AES was demonstrated as a surface scientific approach to assess the alloying of ZnMgO. With gas sensors, I discovered the rf-sputtered anatase-TiO2 thin films for a selective and sensitive NO2 detection at room temperature, under UV illumination. The implementation of UV enhances the responsivity, response and recovery rate of the TiO2 sensor towards NO2 significantly. Evident from the high resolution XPS and AFM studies, the surface contamination and morphology of the thin films degrade the gas sensing response. I also demonstrated that surface additive metal nanoparticles on thin films can improve the response and the selectivity of oxide based sensors. I employed nanometer-scale scanning probe microscopy to study a novel gas senor scheme consisting of gallium nitride (GaN) nanowires with functionalizing oxides layer. The results suggested that AFM together with EFM is capable of discriminating low-conductive materials at the nanoscale, providing a nondestructive method to quantitatively relate sensing response to the surface morphology.

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Despite record-setting performance demonstrated by superconducting Transition Edge Sensors (TESs) and growing utilization of the technology, a theoretical model of the physics governing TES devices superconducting phase transition has proven elusive. Earlier attempts to describe TESs assumed them to be uniform superconductors. Sadleir et al. 2010 shows that TESs are weak links and that the superconducting order parameter strength has significant spatial variation. Measurements are presented of the temperature T and magnetic field B dependence of the critical current Ic measured over 7 orders of magnitude on square Mo/Au bilayers ranging in length from 8 to 290 microns. We find our measurements have a natural explanation in terms of a spatially varying order parameter that is enhanced in proximity to the higher transition temperature superconducting leads (the longitudinal proximity effect) and suppressed in proximity to the added normal metal structures (the lateral inverse proximity effect). These in-plane proximity effects and scaling relations are observed over unprecedentedly long lengths (in excess of 1000 times the mean free path) and explained in terms of a Ginzburg-Landau model. Our low temperature Ic(B) measurements are found to agree with a general derivation of a superconducting strip with an edge or geometric barrier to vortex entry and we also derive two conditions that lead to Ic rectification. At high temperatures the Ic(B) exhibits distinct Josephson effect behavior over long length scales and following functional dependences not previously reported. We also investigate how film stress changes the transition, explain some transition features in terms of a nonequilibrium superconductivity effect, and show that our measurements of the resistive transition are not consistent with a percolating resistor network model.

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The incorporation of graphitic compounds such as carbon nanotubes (CNTs) and graphene into nano-electronic device packaging holds much promise for waste heat management given their high thermal conductivities. However, as these graphitic materials must be used in together with other semiconductor/insulator materials, it is not known how thermal transport is affected by the interaction. Using different simulation techniques, in this thesis, we evaluate the thermal transport properties - thermal boundary conductance (TBC) and thermal conductivity - of CNTs and single-layer graphene in contact with an amorphous SiO2 (a-SiO2) substrate. First, the theoretical methodologies and concepts used in our simulations are presented. In particular, two concepts are described in detail as they are necessary for the understanding of the subsequent chapters. The first is the linear response Green-Kubo (GK) theory of thermal boundary conductance (TBC), which we develop in this thesis, and the second is the spectral energy density method, which we use to directly compute the phonon lifetimes and thermal transport coefficients. After we set the conceptual foundations, the TBC of the CNT-SiO2 interface is computed using non- equilibrium molecular dynamics (MD) simulations and the new Green-Kubo method that we have developed. Its dependence on temperature, the strength of the interaction with the substrate, and tube diameter are evaluated. To gain further insight into the phonon dynamics in supported CNTs, the scattering rates are computed using the spectral energy density (SED) method. With this method, we are able to distinguish the different scattering mechanisms (boundary and CNT-substrate phonon-phonon) and rates. The phonon lifetimes in supported CNTs are found to be reduced by contact with the substrate and we use that lifetime reduction to determine the change in CNT thermal conductivity. Next, we examine thermal transport in graphene supported on SiO2. The phonon contribution to the TBC of the graphene-SiO2 interface is computed from MD simulations and found to agree well with experimentally measured values. We derive the theory of remote phonon scattering of graphene electrons and compute the heat transfer coefficient dependence on doping level and temperature. The thermal boundary conductance from remote phonon scattering is found to be an order of magnitude smaller than that of the phonon contribution. The in-plane thermal conductivity of supported graphene is calculated from MD simulations. The experimentally measured order of magnitude reduction in thermal conductivity is reproduced in our simulations. We show that this reduction is due to the damping of the flexural (ZA) modes. By varying the interaction between graphene and the substrate, the ZA modes hybridize with the substrate Rayleigh modes and the dispersion of the hybridized modes is found to linearize in the strong coupling limit, leading to an increased thermal conductance in the composite structure.

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X-Ray Powder Diffraction (XRPD) laboratory is a facility placed at Servicios Centrales de apoyo a la Investigación (SCAI) at University of Malaga (UMA) http://www.scai.uma.es/. This facility has three XRPD diffractometers and a diffractometer to measure high-resolution thin-films. X´Pert PRO MPD from PANalytical. This is a bragg-brentano (theta/2theta) with reflection geometry diffractometer which allows to obtain high resolution XRPD data with strictly monochromatic CuKα1 radiation (λ=1.54059Å) [Ge(111) primary monochromator] and an automatic sample charger. Moreover, it has parallel monochromatic CuKα1 radiation (λ=1.54059Å) with an hybrid Ge(220) monochromator for capillary and multiproposal (bulk samples up to 1 Kg) sample holders. The HTK1200N chamber from Anton Paar allows collecting high resolution high temperature patterns. EMPYREAN from PANalytical. This diffractometer works in reflection and transmission geometries with theta/theta goniometer, using CuKα1,2 radiation (λ=1.5418Å), a focusing X-ray mirror and a ultra-fast PIXCEL 3D detector with 1D and 2D collection data modes (microstructural and preferred orientation analysis). Moreover, the TTK450N chamber allows low temperature and up to 450ºC studies. A D8 ADVANCE (BRUKER) was installed in April 2014. It is the first diffractometer in Europe equipped with a Johansson Ge(111) primary monochromator, which gives a strictly monochromatic Mo radiation (λ=0.7093 Å) [1]. It works in transmission mode (with a sample charger) with this high resolution configuration. XRPD data suitable for PDF (Pair Distribution Function) analysis can be collected with a capillary sample holder, due to the high energy and high resolution capabilities of this diffractometer. Moreover, it has a humidity chamber MHC-trans from Anton Paar working on transmission mode with MoKα1 (measurements can be collected at 5 to 95% of relative humidity (from 20 to 80 ºC) and up to 150ºC [2]). Furthermore, this diffractometer also has a reaction chamber XRK900 from Anton Paar (which uses CuKα1,2 radiation in reflection mode), which allows data collection from room temperature to 900ºC with up to 10 bar of different gases. Finally, a D8 DISVOVER A25 from BRUKER was installed on December 2014. It has a five axis Euler cradler and optics devices suitable for high resolution thin film data collection collected in in-plane and out-of-plane modes. To sum up, high-resolution thin films, microstructural, rocking-curve, Small Angle X-ray Scattering (SAXS), Grazing incident SAXS (GISAXS), Ultra Grazing incident diffraction (Ultra-GID) and microdiffraction measurements can be performed with the appropriated optics and sample holders. [1] L. León-Reina, M. García-Maté, G. Álvarez-Pinazo, I. Santacruz, O. Vallcorba, A.G. De la Torre, M.A.G. Aranda “Accuracy in Rietveld quantitative phase analysis: a comparative study of strictly monochromatic Mo and Cu radiations” J. Appl. Crystallogr. 2016, 49, 722-735. [2] J. Aríñez-Soriano, J. Albalad, C. Vila-Parrondo, J. Pérez-Carvajal, S. Rodríguez-Hermida, A. Cabeza, F. Busqué, J. Juanhuix, I. Imaz, Daniel Maspoch “Single-crystal and humidity-controlled powder diffraction study of the breathing effect in a metal-organic framework upon water adsorption/desorption” Chem. Commun., 2016, DOI: 10.1039/C6CC02908F.

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The rural electrification is characterized by geographical dispersion of the population, low consumption, high investment by consumers and high cost. Moreover, solar radiation constitutes an inexhaustible source of energy and in its conversion into electricity photovoltaic panels are used. In this study, equations were adjusted to field conditions presented by the manufacturer for current and power of small photovoltaic systems. The mathematical analysis was performed on the photovoltaic rural system I- 100 from ISOFOTON, with power 300 Wp, located at the Experimental Farm Lageado of FCA/UNESP. For the development of such equations, the circuitry of photovoltaic cells has been studied to apply iterative numerical methods for the determination of electrical parameters and possible errors in the appropriate equations in the literature to reality. Therefore, a simulation of a photovoltaic panel was proposed through mathematical equations that were adjusted according to the data of local radiation. The results have presented equations that provide real answers to the user and may assist in the design of these systems, once calculated that the maximum power limit ensures a supply of energy generated. This real sizing helps establishing the possible applications of solar energy to the rural producer and informing the real possibilities of generating electricity from the sun.

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