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

Schrödinger-type wave equations with logarithmic nonlinearity occur in hydrodynamic models of Korteweg-type materials capillarity and surface tension, which can undergo liquid–solid or liquid–gas phase transitions. One the predictions theory is a periodic pattern density inhomogeneities occurring form either bubbles (topological phase), cells (non-topological phase). Such are described by solitonic solutions equation, gaussons kinks, vicinity transition. During solidification process, these become centers nucleation, thus shaping polycrystalline structure metal grains. The predicts Gaussian profile material inside such cell, should manifest Gaussian-like microhardness grain. We report experimental evidence large-scale periodicity grains ferrite steel S235/A570, copper C-Cu/C14200, austenite X10CrNiTi18-10/AISI 321, aluminum–magnesium alloy 5083/5056; also profiles an averaged grain materials.