论文标题
多晶金属中的对数波动效应：理论和实验
Logarithmic wave-mechanical effects in polycrystalline metals: Theory and experiment
论文作者
论文摘要
具有对数非线性的Schrodinger-type波方程在具有毛细血管和表面张力的Korteweg型材料的流体动力模型中发生，这可以经历液态固醇或液态 - 气相变。该理论的预测之一是以一种气泡（拓扑相）或细胞（非探针阶段）形式发生的密度不均匀性的周期性模式。这种不均匀性是通过对数波方程，高森和扭结的孤子解中描述的，在液态相变的附近。在凝固过程中，这些不均匀性成为成核的中心，从而塑造了金属晶粒的多晶结构。该理论预测了这种细胞内部材料密度的高斯曲线，该材料密度应该体现在晶粒内部的微硬度的高斯样曲线中。我们报告了铁氧体钢S235/A570，铜C-Cu/C14200，钢X10CRNITI18-10/AISI 321中的奥斯丁岩的大规模周期性的实验证据，以及铝含量5083/50556；以及这些材料中平均谷物内的微值的高斯样轮廓。
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.
