Discrete temperature values in the sintering process as a BaTiO3-ceramics properties parameter
In this paper, we develop the new physical-mathematical time scale approach-model applied to BaTiO3-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 numb...
Saved in:
| Published in: | Science of sintering Vol. 49; no. 4; pp. 469 - 477 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
International Institute for the Science of Sintering, Beograd
2017
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we develop the new physical-mathematical time scale
approach-model applied to BaTiO3-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),
bio-chemical 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,
BaTiO3-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.
nema |
|---|---|
| ISSN: | 0350-820X 1820-7413 |
| DOI: | 10.2298/SOS1704469V |