Logarithmic Wave-Mechanical Effects in Polycrystalline Metals: Theory and Experiment
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Date
2021
Journal Title
Journal ISSN
Volume Title
Publisher
Springer-Verlag
Abstract
EN: Schro¨dinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Kortewegtype
materials with capillarity and surface tension, which can undergo liquid–solid or liquid–gas phase transitions. One of
the predictions of the theory is a periodic pattern of density inhomogeneities occurring in the form of either bubbles
(topological phase), or cells (non-topological phase). Such inhomogeneities are described by solitonic solutions of a
logarithmic wave equation, gaussons and kinks, in the vicinity of the liquid–solid phase transition. During the solidification
process, these inhomogeneities become centers of nucleation, thus shaping the polycrystalline structure of the metal grains.
The theory predicts a Gaussian profile of material density inside such a cell, which should manifest in a Gaussian-like
profile of microhardness inside a grain. We report experimental evidence of large-scale periodicity in the structure of grains
in the ferrite steel S235/A570, copper C-Cu/C14200, austenite in steel X10CrNiTi18-10/AISI 321, and aluminum–magnesium
alloy 5083/5056; and also Gaussian-like profiles of microhardness inside an averaged grain in these materials.
Description
V. Kraieva: ORCID 0000-0002-9350-5408
Keywords
wave mechanics, polycrystalline metals, logarithmic korteweg material, solidification, microstructure, КФ
Citation
Kraiev M., Domina K., Kraieva V., Zloshchastiev K. G. Logarithmic Wave-Mechanical Effects in Polycrystalline Metals: Theory and Experiment. Indian Journal of Physics. 2021. DOI: 10.1007/s12648-021-02190-2.