Discrete temperature values in the sintering process as a BaTiO3-ceramics properties parameter

Abstract

In this paper, we develop the new physical-mathematical time scale approach-model applied to BaTiO 3 -ceramics. At the beginning, a time scale is defined to be an arbitrary closed subset of the real numbers R, with the standard inherited topology. The time scale mathematical examples include real numbers R, natural numbers N, integers Z, the Cantor set (i.e. fractals), and any finite union of closed intervals of R. Calculus on time scales (TSC) was established in 1988 by Stefan Hilger. TSC, by construction, is used to describe the complex process. This method may be utilized for a description of physical, material (crystal growth kinetics, physical chemistry kinetics -for example, kinetics of barium-titanate synthesis), biochemical or similar systems and represents a major challenge for nowadays contemporary scientists. Generally speaking, such processes may be described by a discrete time scale. Reasonably it could be assumed that such a "scenario" is possible for discrete temperature values as a consolidation parameter which is the basic ceramics description properties. In this work, BaTiO 3 -ceramics discrete temperature as thermodynamics parameter with temperature step h and the basic temperature point a is investigated. Instead of derivations, it is used backward differences with respect to temperature. The main conclusion is made towards ceramics materials temperature as description parameter.

Evolution of structural and functional properties of the Fe/BaTiO3 system guided by mechanochemical and thermal treatment

“…Transition metal doping is a good way to induce magnetism in otherwise non-magnetic barium titanate, with the incorporation of dopants into the BTO lattice largely determined by the ionic radii of the participants in the process [11]. Albeit comprehensively investigated over the years, BTO-based ceramics persist to inspire novel research approaches [12,13] remaining at the forefront of materials science.…”

Sintering effect on electrical properties and morphology of lead-free Na0.92k0.08NbO3 ceramics

“…Perovskite (having ABO 3 structure) type ferroelectrics are the most typical displacive ferroelectrics, e.g., BaTiO 3 , KNbO 3 , PbTiO 3 , KTiO 3 , PbZrO 3 , LiNbO 3 , LiTaO 3 , etc. [2,3]. The ABO 3 type compounds have excellent dielectric, ferroelectric, optical and piezoelectric properties, which have attracted considerable attention of researchers worldwide due to their broad range of technical applications [4][5][6].…”