Logarithmic wave-mechanical effects in polycrystalline metals: Theory and experiment

TL;DR

This paper explores the theoretical prediction and experimental validation of wave-mechanical effects, specifically logarithmic nonlinearities, influencing the microstructure and hardness profiles in polycrystalline metals during phase transitions.

Contribution

It introduces a novel theory linking logarithmic wave equations to polycrystalline structure formation and provides experimental evidence across various metals supporting the predictions.

Findings

Periodic grain structure observed in multiple metals.

Gaussian microhardness profiles within grains confirmed.

Theoretical model aligns with experimental microstructure data.

Abstract

Schrodinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type 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 aluminium-magnesium alloy 5083/5056; and also Gaussian-like profiles of microhardness inside an averaged grain in these materials.