Application of Newton's method for precise calculation of parent orientation and orientation relationship from orientations of daughter phase

摘要

AbstractFor any quantitative study on microstructure of a product phase, information on the parent orientation and orientation relationship is essential, yet it is often lost after phase transformation. Even a numerical approach to the problem was proposed elsewhere, a description of the method used for numerical fitting, its efficiency and accuracy has not been reported so far. Here, we address in details the use of Newton's method as one of the fastest convergence techniques for least squares fitting of parent orientation and orientation relationship from EBSD data of the product phase. A robust algorithm with high precision is proposed in a form convenient for programming. Calculation errors, which are evaluated by a novel approach based on simulation of the daughter orientations, are 0.02° for parent orientation and 0.06° for orientation relationship.Graphical AbstractDisplay OmittedHighlights?Fitting of parent orientation and orientation relationship by using Newton's method?The method is applicable to any type of coherent transformation.?A robust algorithm with high precision is detailed.?Calculation errors were evaluated through simulation of the daughter orientations.?Errors may be as small as 0.02° for parent orientation and 0.06° for orientation relationship.]]>