Acoustic Nonlinearity Parameters Due to Microstructural Defects

This study presents a general approach to derive the acoustic nonlinearity parameters induced by various types of dislocation configurations including dislocation strings (monopoles), dislocation dipoles, dislocation pileups and extended dislocations. It is found that expressions of the acoustic nonlinearity parameter induced by such a variety of dislocation configurations share a common mathematical form. They are all scaled with Lch/bn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {L_{\mathrm{ch}} /b} \right) ^{n}$$\end{document}, where Lch\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm{ch}} $$\end{document} is a characteristic length of the dislocation configuration, b is the magnitude of the Burgers vector, and n is either 3 or 4. Semiquantitative analysis is presented to compare the magnitudes of the acoustic nonlinearity parameters among different types of dislocation configurations.