Near Atomic Row Matching in the Interface Analyzed in Both Direct and Reciprocal Space

Abstract

Reproducible crystallographic features between new phase and matrix are often observed during phase transformation, including orientation relationship, interfacial orientation, morphology, and so on. The geometrical matching in the interface is the key to understanding the preferred transformation crystallography. Recently, a new geometrical method emphasizing the atomic row matching in the interface, the so-called near row matching method, has been proposed to predict the preferred orientations between two arbitrary crystals. In this work, this method originally expressed in direct space was further extended to the reciprocal space. These two methods were implemented in our free software PTClab (version 1.19). It is found that these two expressions are nearly equivalent. As the near row matching in reciprocal space could be directly measured by the diffraction patterns with transmission electron microscopy (TEM), the condition of atomic row matching would be easily identified in reciprocal space during TEM work, and could be applied to rationalize the experimental observations. Several examples in bothsmall and large misfit alloy systems are shown to apply the near tow matching method in both direct and reciprocal space. Furthermore, the row matching method is compared with other models, and there are some crucial aspects that need extra attention when being applied to prediction.