Fractals, Materials and Energy Technologies

World’s perennial need for energy yields the whole spectra of technological challenges and scientific tasks. An important stream in finding new solutions leads over materials characterized by precise microstructural architecture based on fractal geometry/analysis covering wide size ranges down to nano scale. Having such a deep geometric hierarchy opens new possibilities in energy storage capacities supported by fractal resources. These novel ideas are natural continuation of some early fractal applications have been used as a tool in energy research, applying on diverse energy technologies, from photovoltaics to fuel cells and carbon capture. All three items that are essential regarding energetic questions, free energy stocks location, energy harvesting and short/ long term energy storage have their specific common points with fractal nature. Also, the concept of energy as physical objects property, share some features characteristic to fractal objects. In other words, fractal, as a crucial concept of modern theoretical-experimental physics is tightly connected with the process of cultivating the wild energy as well. Here, the above items will be discussed. The term “geometry” as it is custom in plain language, understands “shape” rather than the science of geometry. In this sense, “geometry” describes property of hierarchy that is more present in every day’s life than we are usually aware of. Just note that all our senses often convey information on the quality of some matter by absorbing certain hierarchical order. The touch feeling of smooth or rough surface, olfactory or taste data differ by energetic level that generates according to geometry of particles or clusters that follow fractal patterns. Adjusting specific, a priori constructed fractal micro or nano architecture make the energetic flow more effective by decrease losses made by non-conformal geometry

Electrical Characteristics of Ho doped BaTiO3 Ceramics

In this paper, electrical characteristics of Ho2O3 doped BaTiO3 ceramics were shown, using new method for measuring samples. The BaTiO3 doped samples were sintered at 1320°C for 4 hours. The concentration of the additives were from 0.05 to 1.0 at% Ho. The density was ranged from 83% to 91% of theoretical density (TD). The samples of BaTiO3 ceramics doped with Ho2O3 are characterized by spherical and irregular polygonal grains. The average grain size for samples doped with low content of Ho2O3 (0.05 at% Ho) ranged from 10 μm to 30 μm. An increase in dopant concentration causes a decrease in the average grain size in the investigated samples. So it is for samples doped with 1.0 at% Ho, grain size range between less than 1 mm – 2 mm. The variation of dielectric permittivity with temperature were measured in the temperature range from 30°C to 180°C and the frequency range from 100 Hz to 1 MHz. For measurement electrical characteristic a new method was used, which implemented to automate the sampling and to enable measurement without a human factor. The software application is connected via USB communication to a microcontroller, which measures the temperature in the furnace. When the temperature reaches the defined value, the microcontroller sends information to the software application. Then the application through GPIB communication activates the LCR meter, which measures the defined parameters of the tested samples. Based on parameters such as dielectric constant (εr), tangent losses (tan δ) and impedance, the characteristics of the tested samples were determined. Using the Curie-Weiss law and modified Curie-Weiss law, based on the measured values of the parameters, the Curie constant and the exponent of nonlinearity were determined

Curie-Weiss Law Fractal Corrections and Clausius-Mossotti Equation

The Clausius–Mossotti relation emerged as a combination of the analysis of indices of refraction (by Rudolf Clausius) and the relationship between the dielectric constants of two different media (Ottaviano-Fabrizio Mossotti). Since it connects dipole’s polarizability with the electric permittivity of a material made of those dipoles, it is one of the fundamental relationship that can be derived from Maxwell’s conductivity equation. Also, it is tightly connected both the Curie and Curie–Weiss laws which are correlation relations. Using fractal approach in Curie–Weiss equation and fractal correction applied recently by the authors, the Clausius–Mossotti relation is also subjected to modification with respect to ferroelectric materials fractal nature. The correction is operationally performed by introducing fractal correction factor a0 > 1, as a multiplier to the usual dielectric constant er to gain the bigger value a0er. This shows that the Clausius–Mossotti relation is also “permeated” by fractal nature being inherited from the material’s morphology. Our experiments were carried out on BaTiO3-ceramics as characteristic representative of perovskites but the conclusions can be applied on any other ceramics materials as well as on thin film layers and coating in general. By shapes control and contact surfaces numbers on the entire BaTiO3-ceramic sample level, the control over structural properties of these ceramics can be done, with the aim of correlation between material electronic properties and corresponding microstructure. The fractal correction has wide consequences on many phenomena like PTC, ferroelectrics, ferromagnetics, piezo- and optoelectronic properties as well as electrochemical thermodynamic and fluid dynamics parameters

Microstructure characterization of porous microalloyed aluminium-silicate ceramics

Kaolinite and bentonite clay powders mixed with active additives, based on Mg(NO3)2 and Al(NO3)2, sintered at high temperatures produce very porous ceramics with microcrystalline and amorphous regions and highly developed metalized surfaces (mainly with magnesium surplus). Microstructure investigations have revealed non-uniform and highly porous structure with broad distribution of grain size, specifically shaped grains and high degree of agglomeration. The ceramics samples were characterized by scanning electron microscopy (SEM), energy dispersive spectrometer (EDS), X-ray diffraction analysis (XRD) and IR spectroscopy analysis, prior and after treatment in “synthetic water”, i.e. in aqueous solution of arsenic-salt. Grain size distribution for untreated and treated samples was done with software SemAfore 4. It has shown great variety in size distribution of grains from clay powders to sintered samples

Jews in the poetry of Raša Livada: how low until we reach the God?

U radu se tumače načelno dva pesnička teksta Raše Livade: „Sinagoga” i „Pismo rabina Alkalaja”. Ostajući u krugu naznačene teme, pesničkog dijaloga sa jevrejskim nasleđem i istorijom, posebno se promatra pitanje konceptualizacije transcendentnog prostora, metafizike leta i, najzad, pitanje nizine/imanencije. Kako je tumačenje procesa ovremenjavanja i oprostoravanja transcendentnog uporišta neodvojivo od grafizma, grafostilematike, biće reči i o metafizičkoj snazi lirske beline. Istovremeno, pod polisemičnim pitanjem o pamćenju nestalih, u praznim hramovima, rabinovim oporukama ispisuje se kartografija Grada kao znak teritorijalne eshatologije i/ili izlaska kao ontološka (blanšoovska) privilegovanost književnosti da iskorači, redefiniše odnose bliskog i dalekog, prisustva i neprisustva.The paper analyzes two poems by R. Livada, “Sinagoga” and “Pismo rabina Alkalaja” from the collection of poems "Karantin" (1977). Searching for the Jews on the lyrical map of Zemun, the question of the concept of transcendent space opens up, as well as the metaphysics of flight and the figure of God. The historical persecution, wandering, and disappearance of Jews in Livada's poetry are poetically and aesthetically shaped as a place of emptiness, but also as a sign of the metaphysics of the City, belonging to the lost Homeland. This symbolic power pervades despite the parodic, ironic discourse and the destabilization of the lyrical form. Finally, what remains is a word like homeland (domus) and, with it, fateful cartographies and signs of the exodus. Relying on M. Heidegger's ontology of space and the theory of M. Blanchot, the position of the low in the conception of lyrical spaces proves to be a challenge to metaphysical metaphors, but also a critique of historic oblivion and terror.Izdavanje ovog zbornika podržalo je Ministarstvo prosvete, nauke i tehnološkog razvoja Republike Srbije

Fractal Corrections of BaTiO3-ceramic Sintering Parameters

Morphology of ceramics grains and pores as well as Brownian character of particle dynamics inside ceramics specimen contributes to better understanding of the sintering process. BaTiO3-ceramics, studied in this paper, has light fractal form and it is emanated in three aspects. First, the surface of grains, even in starting green body as well as distribution of grains shows fractal behavior. Second, existence of pores and their distribution follow the rules of fractal geometry. Third, movement of particles inside viscous flow underlies the rule of Brownian motion, which is essentially a fractal category. These three elements, each in its domain influence sintering dynamics, and can be described by dimensionless quantitative factors, alpha(S), alpha(P) and alpha(M), being normalized to the interval [0,1]. Following sintering process, the associate formulae of Frenkel, Scherer and Mackenzie-Shuttleworth are shown from the angle of view of ceramics fractal dimension changing that approaches to 3. Also, it is shown that the energy balance is not violated after applying fractal correction to quasi equilibrium of the energy emanating from surface area reduction E-S and energy adopted by viscous flow E-f

Application of the intergranular impedance model in correlating microstructure and electrical properties of doped BaTiO3

Microstructure properties of barium-titanate based materials, expressed in grain boundary contacts, are of basic importance for electric properties of this material. In this study, the model of intergranular impedance applied on a two-grain contact is considered. Globally, a BaTiO3-ceramics sample consists of a large number of mutually contacted grains, which form clusters. Such clusters can be presented as specific fractal formations. For each of them, it is possible to establish the equivalent electrical model and, for a defined set of input parameters, using symbolic analysis, obtain the frequency diagram. The influence of fractal structure is especially stressed. Realizing the totality of relations between cluster grain groups, their microelectrical schemes and corresponding frequency characteristics, on one hand, and the global equivalent electrical scheme and corresponding acquired frequency characteristics of BaTiO3-ceramics samples, on the other hand, we set a goal of correlating experimental results with the summing effect of microelectric equivalent schemes. The model is successfully tested on doped barium-titanate ceramics.Mikrostrukturna svojstva materijala na bazi barijum-titanata, izražena kontaktima granica zrna od fundamentalne su važnosti za električna svojstva ovih materijala. U ovom radu razmatrana je primena modela impedanse između dva zrna na kontakt dva zrna. Globalno posmatrano, uzorak BaTiO3-keramike sastoji se od ogromnog broja zrna u međusobnom kontaktu koji formiraju klastere. Takvi klasteri mogu biti predstavljeni kao specifične fraktalne formacije. Za svaku od ovih formacija moguće je uspostaviti ekvivalentni električni model za definisani set ulaznih parametara koristeći metod simboličke analize i dobiti odgovarajuću frekventnu karakteristiku. Posebno je naglašen uticaj fraktalne strukture. Realizujući kompletnu relaciju između klastera zrna, njihovih mikroelektričnih šema i odgovarajućih frekventnih karakteristika s jedne strane, i globalnih ekvivalentnih električnih šema i odgovarajućih frekventnih karakteristika uzoraka BaTiO3-keramike, s druge strane, uspostavljamo set ciljanih koincidentnih eksperimentalnih rezultata sa sumarnim efektima izračunavanih mikroelektričnih ekvivalentnih šema. Model je uspešno testiran na uzorcima barijum-titanatne keramike

Sintering Process Influence on Microstructure and Intergranular Impedance of Rare-Earth Modified BaTiO3-Ceramics

Sintering process is a complex of different synergetic effects during the ceramics materials consolidation. The microstructural level properties control is very important as a stage in advanced materials prognosis. SEM analysis of Yb/BaTiO3 doped ceramics showed that in samples doped with, a low level of dopant and sintered at higher temperatures the grain size ranged from 10-60 mu m, while with the higher dopant concentration the grain, size ranged between 2-15 mu m. The morphology of sintered BaTiO3-ceramics grains points out the validity of developing new structure analytical methods based on different geometries of grains' model systems. The idea of electrical properties of BaTiO3-ceramics being influenced by intergrain microcontacts can be successfully followed if we start with the two-sphere Coble's model and also the correction of the Coble's model. In this paper, the grains contact models based on spherical, ellipsoidal and polyhedral geometries are presented making a new modeling tool for structure research of BaTiO3-ceramics materials. Intergranular impedance analysis of grains clusters was also introduced. Obtained results enabled establishment of interrelation between. structural and electrical parameters

Quantitative metallography modern metods

This paper has been concerned with the classical Stereological targets V, S, L, and N only, namely with so-called first-order properties. Stereology is now drifting rapidly toward second-order methods, aimed at quantifying spatial pattern for the elements of a structure (e.g. clustering, repulsion, etc., between the elements) as well as the nature and degree of association between different structures. Second-order statistical methods are widely available for point patterns. Important devices for the second-order analysis of cells and organelles when regarded as points in space have recently been devised. Analogous methods extend to higher dimensional quantities such as surface areas and volumes

Fractal nature Heywang model correction and Brownian motions

Ceramics grains contacts are essential for understanding complex dielectric properties of electronic ceramics materials. Since the actual contact surface is an irregular object, the theory of fractal sets is applied. Also, the Heywang model of intergranular capacity are introduced as a basic idea for relations with fractal structure. The BaTiO3-ceramics has fractal form in, at least, two levels: shapes and distributions of grains and intergranular contacts. Using fractal modeling approach, reconstruction of microstructure, like shapes of grains or intergranular contacts can be successfully done. Furthermore, the area of grains surface is calculated by using fractal correction that expresses the irregularity of grains surface through fractal dimension. It is known that BaTiO3 and similar ceramics have fractal nature based on three different phenomena. First, there is process of Brownian-fractal motions inside the material during sintering in the form of flowing micro-particles –ions, atoms, electrons which is an essentially fractal phenomena. This motion has fractal structure and can be undergo the process of fractal modification. Second, there are so called “negative space” made of pores and intergranular space. Being extremely complex, the pore space plays an important role in microelectronic, PTC and other phenomena. Third, ceramic grains have fractal shape seeing as a contour in cross section or as grain’s surface. These triple factors, in combination, make the microelectronic environment of very peculiar electro-static and dynamics microelectronic environment. In order to obtain an equivalent circuit model, which provides a more realistic representation of the electronic materials electrical properties, in this article an intergranular contacts model for the BaTiO3 electrical properties characterization were determined and implemented. Considering obtained results, the directions of possible BaTiO3-ceramics materials properties prognosis are determined according to the correlations synthesisstructure- properties