A Mathematical Model for Simulation of Intergranular μ-Capacitance as a Function of Neck Growth in Ceramic Sintering

Branislav M. Randjelović and Zoran S. Nikolić ()
Additional contact information
Branislav M. Randjelović: University of Niš
Zoran S. Nikolić: University of Niš

A chapter in Computational Mathematics and Variational Analysis, 2020, pp 403-420 from Springer

Abstract: Abstract In this paper we will define a new mathematical model for predicting an evolution of an equivalent intergranular μ-capacitance during ceramic sintering. The contact between two adjacent grains will be defined as a structure that forms a μ-capacitor recognized as an intergranular μ-capacitor unit. It will be assumed that its μ-capacitance changes as the neck grows by diffusion. Diffusion mechanisms responsible for transport matter from the grain boundary to the neck are the volume diffusion and grain boundary diffusion. Such model does not need special geometric assumptions because the microstructural development can be simulated by a set of simple local rules and overall neck growth law which can be arbitrarily chosen. To find the total capacitance we will identify μ-capacitors in series and in parallel. More complicated connections of μ-capacitors will be transformed into simpler structure using delta to star transformation and/or star to delta transformation. In this way some μ-capacitors will be step-by-step replaced by their equivalent μ-capacitors. The developed model can be applied for the prediction of an evolution of the intergranular capacitance during ceramic sintering of BaTiO3 system with spherical particle distributions.

Date: 2020
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-44625-3_22

Ordering information: This item can be ordered from
http://www.springer.com/9783030446253

DOI: 10.1007/978-3-030-44625-3_22

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().